2023/04/27 by Aniruddha Biswas, Palash Sarkar, Biswas, Aniruddha +1
Computer Science · #Advanced Algebra and Logic #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2304.14069
We show that the problem of counting the number of n-variable unate functions reduces to the problem of counting the number of n-variable monotone functions. Using recently obtained results on n-variable monotone functions, we obtain counts of n-variable unate functions up to n=9. We use an enumeration strategy to obtain the number of n-variable balanced monotone functions up to n=7. We show that the problem of counting the number of n-variable balanced unate functions reduces to the problem of counting the number of n-variable balanced monotone functions, and consequently, we obtain the number of n-variable balanced unate functions up to n=7. Using enumeration, we obtain the numbers of equivalence classes of n-variable balanced monotone functions, unate functions and balanced unate functions up to n=6. Further, for each of the considered sub-class of n-variable monotone and unate functions, we also obtain the corresponding numbers of n-variable non-degenerate functions.